Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solut...

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Autores principales: Bankmann, Daniel, Mehrmann, Volker, Nesterov, Yurii, Van Dooren, Paul
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Singapore 2020
Materias:
Original Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7677160/
https://www.ncbi.nlm.nih.gov/pubmed/33240968
http://dx.doi.org/10.1007/s10013-020-00427-x
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author Bankmann, Daniel
Mehrmann, Volker
Nesterov, Yurii
Van Dooren, Paul
author_facet Bankmann, Daniel
Mehrmann, Volker
Nesterov, Yurii
Van Dooren, Paul
author_sort Bankmann, Daniel
collection PubMed
description In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.
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spelling pubmed-76771602020-11-23 Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis Bankmann, Daniel Mehrmann, Volker Nesterov, Yurii Van Dooren, Paul Vietnam J Math Original Article In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples. Springer Singapore 2020-07-23 2020 /pmc/articles/PMC7677160/ /pubmed/33240968 http://dx.doi.org/10.1007/s10013-020-00427-x Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Original Article
Bankmann, Daniel
Mehrmann, Volker
Nesterov, Yurii
Van Dooren, Paul
Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
title Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
title_full Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
title_fullStr Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
title_full_unstemmed Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
title_short Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
title_sort computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7677160/
https://www.ncbi.nlm.nih.gov/pubmed/33240968
http://dx.doi.org/10.1007/s10013-020-00427-x
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